My (m28) GF (f25) is too confident. Its causing issues in our relationship

My Girlfriend is a scientist. Of which I am proud of.
We've had our ups and downs but I love her more than anything. The problem, if I could even call it that, is that she is too confident.
She has strong opinions about others and considered herself better and more intelligent than others. Because of her profession and background.
The other day she was talking about how she was gonna win this award because everyone else was dumb and she's the only one at work with a clue. And sure enough, she DID win.
It's not always "this". I don't wanna misrepresent her. But the way she talks about people and how confident she is can be really odd and sometimes cruel. Eg. She's really dismissive of people very quickly. Some of my friends and family included. And yes I've talked to her about this.
But It's never been a really big problem for us as I DO think she's special and I always back her. She truly is amazing.
The problem is showing itself in our relationship though. When we argue, she never backs down. Even when she is Clearly wrong. Even over simple stuff. It's like she just expects me too agree with her. She's even said, that it "bothers" her when we disagree.
I wanna keep backing her. Boosting her up. Making her feel special and smart because she truly is kickass. And I guess she needs that armour in her field and job.
I just want her to not dismiss my feelings or opinions.
How can I speak to her about this without making her feel I'm diminishing her?
Tl;dr: My girlfriend is amazing but also sometimes incredibly cruel. These things are sometimes related. How can I have the former and not the later.


Source.